Question

for the given figure, can you conclude m || n? justify your reasoning.choose the correct answer below.a. no, line m is not parallel to line n because the labeled angles are congruent, but they are not alternate interior angles.b. yes, m || n because the labeled angles are supplementary alternate interior angles.c. no, line m is not parallel to line n because the labeled angles are alternate interior angles, but they are not congruent.d. yes, m || n because the labeled angles are congruent alternate interior angles.

Explanation:

First, identify the labeled angles as alternate interior angles formed by transversal \(t\) with lines \(m\) and \(n\). For two lines to be parallel, alternate interior angles must be congruent. Here, the angles are \(88^\circ\) and \(87^\circ\), which are not equal. Thus, lines \(m\) and \(n\) are not parallel.

Answer:

C. No, line m is not parallel to line n because the labeled angles are alternate interior angles, but they are not congruent.